Combining rendered images to increase samples
From the linked answer (https://blender.stackexchange.com/a/21809) you have the following image to show the compositor node setup :



As mentioned in the correction to the linked answer, the Mix factors are actually incorrect - the correct values are as you stated : (100%), 50%, 33%, 25%, 20%, for 5 images (where the 100% corresponds to the first image which shares the mix node with the second image).

While this might intuitively seem wrong, it is actually correct due to how the images higher up the chain actually proliferate through multiple Mix nodes.

Consider the four images A, B, C, D.

Starting at the last image 'mixed', this is included with a mix factor of 25%. As expected, this will contribute 25% to the final result. This means that 75% of the final result will be contributed to by the remaining 3 images (A, B, C).

Final Result = 25% of D + 75% of (A, B, C)


Now considering the next image (C), this will contribute 33%, meaning that A and B contribute the remaining 67% (actually 33.33333% and 66.66666% would be more accurate) :

Final Result = 25% of D + 75% of (33% of C + 66% of (A,B))


For the final mix, 50% is contributed by B and the remainder (50%) is contributed by A (we don't need to bother with the 100% since that's purely A) :

Final Result = 25% of D + 75% of (33% of C + 66% of (50% of B + 50% of A))


All we've done so far is expand the mix nodes to represent the percentage of each output that contributes to the output, bearing in mind that the two percentages must add up to 100% (so if one image contributes 'x'% then the other must contribute '100-x'%).

Now, we can multiply the percentages into the braces to expand as follows :

Final Result = 25% of D + 75% of (33% of C + (66% of 50% of B) + (66% of 50% of A))
             = 25% of D + 75% of (33% of C + 33% of B + 33% of A)
             = 25% of D + (75% of 33% of C) + (75% of 33% of B) + (75% of 33% of A)
             = (25% of D) + (25% of C) + (25% of B) + (25% of A)


i.e. Because the Mix nodes are chained together, the 100%, 50%, 33%, 25% factors combine to result in each input image contributing to 25% of the resultant image.

As mentioned in the linked answer, the same result could be achieved by using Add nodes to add the images together and dividing the result by 4.

i.e. Mix nodes (note the reducing Factors) :



Is equivalent to Add and Divide nodes (again, note the Factors set to 1.0) :